Analysis of Rayleigh Taylor instability in nanofluids with rotation

Pooja Girotra; Jyoti Ahuja; Dinesh Verma

doi:10.3934/naco.2021018

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2022, Volume 12, Issue 3: 495-512. Doi: 10.3934/naco.2021018

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Analysis of Rayleigh Taylor instability in nanofluids with rotation

1.
Research Scholar, Deparment of Mathematics, NIILM University, Kaithal, Haryana, India
2.
Department of Mathematics, Post Graduate Government College, Sector-11, Chandigarh, India
3.
Department of Mathematics, NIILM University, Kaithal, Haryana, India

^* Corresponding author: jyotiahuja1985@gmail.com
^* Corresponding author: jyotiahuja1985@gmail.com

Received: November 30, 2020

Revised: March 31, 2021

Early access: May 2021

Published: September 2022

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Abstract

This article focuses on the hidden insights about the Rayleigh-Taylor instability of two superimposed horizontal layers of nanofluids having different densities in the presence of rotation factor. Conservation equations are subjected to linear perturbations and further analyzed by using the Normal Mode technique. A dispersion relation incorporating the effects of surface tension, Atwood number, rotation factor and volume fraction of nanoparticles is obtained. Using Routh-Hurtwitz criterion the stable and unstable modes of Rayleigh-Taylor instability are discussed in the presence/absence of nanoparticles and presented through graphs. It is observed that in the absence/presence of nanoparticles, surface tension helps to stabilize the system and Atwood number has a destabilizing impact without the consideration of rotation factor. But if rotation parameter is considered (in the absence/presence of nanoparticles) then surface tension destabilizes the system while Atwood number has a stabilization effect (for a particular range of wave number). The volume fraction of nanoparticles destabilizes the system in the absence of rotation but in the presence of rotation the stability of the system is significantly stimulated by the nanoparticles.

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Mathematics Subject Classification: Primary: 76E99; 76U99;.

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Figure 1. Effect of surface tension on growth rate parameter of Rayleigh Taylor instability in the absence of nanoparticles with rotation and without rotation for varying T = 0.1, 0.2

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Figure 2. Effect of Atwood number on growth rate parameter of Rayleigh Taylor instability in the absence of nanoparticles with rotation and without rotation for varying A = 0.11, 0.119

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Figure 3. Effect of rotation parameter on growth rate parameter of Rayleigh Taylor instability in the absence of nanoparticles with rotation and without rotation for varying $ \Omega $ = 0.1, 0.2, 0.3

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Figure 4. Effect of surface tension on growth rate parameter of Rayleigh Taylor instability in the presence of same kind of nanoparticles with rotation and without rotation for varying T = 0.0001, 0.0002

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Figure 5. Effect of Atwood number on growth rate parameter of Rayleigh Taylor instability in the presence of same kind of nanoparticles with rotation and without rotation for varying A = 0.11, 0.119

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Figure 6. Effect of volume fraction of nanoparicles on growth rate parameter of Rayleigh Taylor instability in the presence of same kind of nanoparticles with rotation and without rotation for varying $ \phi $ = 0.001, 0.005

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Figure 7. Effect of rotation number on growth rate parameter of Rayleigh Taylor instability in the presence of same kind of nanoparticles $ \Omega $ = 0.1, 0.2, 0.3

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Figure 8. Effect of surface tension on growth rate parameter of Rayleigh Taylor instability in the presence of different kind of nanoparticles with rotation and without rotation for varying T = 0.0001, 0.0002

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Figure 9. Effect of Atwood number on growth rate parameter of Rayleigh Taylor instability in the presence of same kind of nanoparticles with rotation and without rotation for varying A = 0.11, 0.119

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Figure 10. Effect of volume fraction of nanoparicles on growth rate parameter of Rayleigh Taylor instability in the presence of different kind of nanoparticles with rotation and without rotation for varying $ \phi $ = 0.001, 0.005

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Figure 11. Effect of rotation number on growth rate parameter of Rayleigh Taylor instability in the presence of diffrent kind of nanoparticles $ \Omega $ = 0.1, 0.2, 0.3

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